PLEASEEE HELP —-> Step 1: Construct a circle through three points not on a line.
a) Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by
drawing line segments DE and EF. Then construct the perpendicular bisectors of DE and EF, and
name the point of intersection of the perpendicular bisectors O. How do you know that point O
is the center of the circle that passes through the three points? (10 points)
Answers
Answer:
Step-by-step explanation:
To show that point O is the center of the circle that passes through points D, E, and F, we can use the property of perpendicular bisectors. The perpendicular bisectors of two chords of a circle bisect the chord and pass through the center of the circle. Since the perpendicular bisectors of DE and EF intersect at point O, it follows that O must be the center of the circle that passes through points D, E, and F.
This property can also be proven using the Pythagorean theorem. Let the radius of the circle be r and let the midpoints of DE and EF be M1 and M2, respectively. Then, OM1 = OM2 = r, and the distance between M1 and M2 is equal to the distance between D and F. By the Pythagorean theorem, the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse, so we have:
OM1^2 + (M1M2)^2 = r^2 + r^2 = 2r^2
Since OM1^2 + (M1M2)^2 is equal to 2r^2, it follows that the distance between M1 and M2 is equal to the diameter of the circle. This means that M1 and M2 are the midpoints of the diameter of the circle, so they must both lie on the circumference of the circle. This, in turn, means that O is the center of the circle that passes through points D, E, and F.
Related Questions
A couch and coffee table cost a total of $1128. The cost of the couch is three times the cost of the coffee table. Find the cost of each item.
cost of couch :
cost of coffee table:
Answers
Answer:
cost of couch: $846
cost of coffee table: $282
Step-by-step explanation:
An angle measures 64.2° more than the measure of its complementary angle. What is the measure of each angle?
Answers
On solving the provided question, we can say that first angle is 37.9° . second angle will be 52.1°.
What are angles?An angle is a fοrm in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a pοint in the middle known as the angle's vertex. In the plane where the rays are placed, twο rays can produce an angle.
An angle is alsο produced when two planes intersect. They're knοwn as dihedral angles. In plane geοmetry, an angle is the form that two rays or lines with a commοn termination might take. The Latin word "angulus," which means "hοrn," is where the English word "angle" comes from. The two rays, also knοwn as the sides of the angle, have a common termination knοwn as the vertex.
x = first angle
Complementary angle is 14.2 degrees more than the cοmplementary angle.
First angle = x
Second angle = x + 14.2°
Complementary angle
x+x+14.2=90
2x+14.290
2x 90 14.2
2x = 75.8 x = 37.9
First angle is 37.9°.
Second angle will be:
x+14.2°
⇒37.9°+ 14.2°
⇒52.1°
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CJ has three more pet pigs than Jacqui has. Let’s write an expression to represent how many pigs CJ has. To do that, we follow these steps:
Identify the constants and the variables.
There is one known number or constant here: it is 3. CJ has 3 more pigs than Jacqui. That number, 3, won’t change. The variable is the number of pets Jacqui has. Let’s call that j.
Identify the operations.
The phrase “more than” tells us we need to add. There are no other operations in this expression.
Rewrite the phrase as an expression.
“Three more pet pigs than Jacqui has” is 3 + j.
Last year, Shailyn read four fewer books than Oswaldo. Which expression shows how many books Shailyn read last year?
Answers
Answer: Let's follow the same steps as in the previous example:
Identify the constants and the variables.
The known constant here is 4. Shailyn read 4 fewer books than Oswaldo. Let's call the number of books Oswaldo read "o".
Identify the operations.
The phrase "four fewer" tells us we need to subtract.
Rewrite the phrase as an expression.
"Four fewer books than Oswaldo" is o - 4.
So, the expression that shows how many books Shailyn read last year is o - 4.
Step-by-step explanation:
Please help quickly!
Answers
Using the rules for matrix multiplication we will see that a₁₂ = 144
How to find the element a₁₂?That would by the second element on the first row of the product matrix.
Remember how the product works, we will get:
a₁₂ = 24*2 + 32*3
a₁₂ = 48 + 96
a₁₂ = 144
The correct option is the last one.
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A typical speed limit in Europe is 50 km/h (kilometers per hour). How fast is that in mph (miles per hour)? Round your answer to one decimal place!
Answers
Answer:
To convert from kilometers per hour to miles per hour, we use the conversion factor of 1 mile per hour = 1.609 kilometers per hour.
So, 50 km/h = 50 x 1.609 mph = 80.45 mph
Rounding to one decimal place, the answer is 80.5 mph.
The typical speed limit in Europe is,
⇒ 833.3 miles per hour.
We have to given that,
A typical speed limit in Europe is, 50 km/h (kilometers per hour).
We can change the speed limit from kilometers per hour in miles per hour.
⇒ 50 kilometers per hour
⇒ 50 × 1000 / 60 miles per hour.
⇒ 50000 / 60 miles per hour.
⇒ 833.3 miles per hour.
Therefore, The typical speed limit in Europe is,
⇒ 833.3 miles per hour.
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please thank you mwaaaaaaaaaaaaa
Answers
The exact perimeter of the segment is 54.13 inches, and the exact area of the segment is 301.44 square inches.
What is perimeter and area enclosed in circle?
A circle is also defined by two properties: area and perimeter. The formulas for both the measures of the circle are given by; Area of a circle = πr². The perimeter of a circle = 2πr.
Let's call the center of the circle O and the endpoint of the arc A. Let's also call the endpoint of the chord that defines the segment B. Then we have an isosceles triangle OAB, where OA = OB = 24 inches.
1) The perimeter of the segment is equal to the length of the arc plus the length of the chord. To find the length of the arc, we can use the formula:
Arc length = (Ф / 360) * 2πr,
where Ф is the measure of the angle in degrees, r is the radius (which is 24 inches in this case), and π is pi.
In this case, the measure of the angle is 60°, so the length of the arc is:
Arc length = (60 / 360) * 2π * 24 inches
Arc length = (1/6) * 2π * 24 inches
Arc length = 4π inches
To find the length of the chord, we can use the formula:
Chord length = 2r * sin(Ф/2), where r is the radius and Ф is the measure of the angle in radians.
First, we need to convert the angle measure from degrees to radians:
60° = 60 * (π / 180) radians = π / 3 radians
Now, we can find the length of the chord:
Chord length = 2 * 24 * sin(π / 6)
Chord length = 24 * 2 * sin(π / 6)
Chord length = 24 * √3 inches
Finally, we can add the length of the arc and the chord to find the perimeter:
Perimeter = 4π + 24 * √3
Perimeter = 4π+41.57
Perimeter = 54.13 inches
2) To find the area of the segment, we can use the formula:
Area = (Ф/ 360) * πr², where Ф is the measure of the angle in degrees and r is the radius.
In this case, the measure of the angle is 60°, so the area of the segment is:
Area = (60 / 360) * π * 24² square inches
Area = (1/6) * π * 576 square inches
Area = 96π square inches
Area = 301.44 square inches
So, The exact perimeter of the segment is 54.13 inches, and the exact area of the segment is301.44 square inches.
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Find the present value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years.
Answers
Answer: The present value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years can be calculated using the formula:
PV = PMT * [ (1 - (1 + r)^-n) / r ] * (1 + r)
where:
PMT = $300 (the monthly payment)
r = 0.06/12 (the monthly interest rate)
n = 10*12 (the number of periods over 10 years, with 12 months in a year)
Plugging in the values into the formula, we get:
PV = $300 * [ (1 - (1 + 0.06/12)^-n) / (0.06/12) ] * (1 + 0.06/12)
PV = $300 * [ (1 - (1 + 0.06/12)^-(10*12)) / (0.06/12) ] * (1 + 0.06/12)
PV = $300 * [ (1 - 1.06^-120) / (0.06/12) ] * (1 + 0.06/12)
PV = $300 * [ (1 - 0.379362539) / (0.06/12) ] * (1 + 0.06/12)
PV = $300 * [ (0.620637561) / (0.06/12) ] * (1 + 0.06/12)
PV = $300 * 10.34300138
PV = $31,029.
So the present value of the annuity due is $31,029. This means that if you were to invest $31,029 today, you would receive a monthly payment of $300 for 10 years at 6% interest compounded monthly.
Step-by-step explanation:
B) The area of a triangle = ½ the base the
height
What is the area of an equilateral triangle where
every side measures 10 cm?
Answers
The area of the equilateral triangle with side length 10 cm is 25 cm².
What is triangle ?
Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.
To find the area of an equilateral triangle, we need to find the height first. The height of an equilateral triangle is equal to the length of the perpendicular line from the center of the triangle to one of its sides.
To find the height, we can divide the equilateral triangle into two 30-60-90 triangles. The height is equal to half of the hypotenuse of one of these triangles, which can be calculated as:
10 cm / 2 = 5 cm
Now that we have the height, we can find the area of the equilateral triangle as follows:
Area = ½ * base * height
Area = ½ * 10 cm * 5 cm
Area = 25 cm²
Hence, The area of the equilateral triangle with side length 10 cm is 25 cm².
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Solve the following polynomial equation. y3+8=0
Answers
please help me with math i’ll give you brainlist
Answers
Answer:we can’t help if it is barely readable
Step-by-step explanation:
4. The first term in the sequence is 5 and the fifth term is 17. What is the common difference?
(1) 2.4
(2) 12
(3) 3
(4) 4
Answers
Answer:
(3) 3
Step-by-step explanation:
Arithmetic Sequence:An arithmetic sequence is a sequence of numbers in which each of them can be defined by adding a common difference to a term to find the next term.
So for example, let the first term, or number be expressed as: [tex]a_1[/tex] and the common difference be expressed as: [tex]d[/tex] That means the second term, or number can be defined as: [tex]a_2=a_1+d[/tex]. If we now add the common difference to the second term, we would get the third term, and so on.
An arithmetic sequence can be compared to that of a linear equation, except it's a sequence of numbers... and also it's restricted to integers greater than zero (starts at first term, second term.... and so on)
So the common difference can be compared to the slope, and we can actually just use the slope formula! The "x" value being the term number, and the "y" value being the term. So the first term in the sequence is 5 can be expressed as: (1, 5) and the fifth term is 17 can be expressed as (5, 17). Now using the slope formula we would get: [tex]d=\frac{17-5}{5-1}=\frac{12}{4}=3[/tex]
Another way to think of it is the first term is 5, and if we add "d" or the common difference to it, we get the second term, if we add another "d" we get the third term, if we another "d" we get the fourth term and if add yet another "d" we get the fifth term. We add a total of four "d's" which can be expressed as: [tex]5+4d[/tex] and this equals the fifth term, but we also know this to be equal to 17, so we can set them equal to each other: [tex]5+4d=17[/tex] now just subtract 5 and divide by 4 to get: [tex]d=3[/tex]
16% of the cows have already had calves. 32 have not had calves yet. How many are in the herd?
Answers
Answer:
There are approximately 38 cows in the herd.
Step-by-step explanation:
In this problem, we are asked to find the number of cows in a herd, given that 16% of the cows have already given birth to calves and 32 have not yet done so.
Assuming there are no other types of cows in the herd, we can determine that the 32 cows that have not had calves make up 84% of the herd, since they are what is left over when 16% is subtracted from 100% (the whole herd).
[tex]100\%-16\% = 84\%[/tex]
We can now create a equation that shows that 84% of the herd is 32 cows, representing the total number of cows in the herd as x.
[tex]32 \text{ cows} = 84\% \cdot x[/tex]
Finally, to solve for the number of cows in the herd, we can multiply both sides by 100/84.
[tex]\dfrac{100}{84}(32 \text{ cows}) = (84\% \cdot x)\dfrac{100}{84}[/tex]
[tex]x \approx 38 \text{ cows}[/tex]
So, there are approximately 38 cows in the herd.
Find the number of positive integers that satisfy both the following conditions:
* Each digit is a 1 or a 2 or a 3
* The sum of the digits is 4.
Answers
The number of positive integers that satisfy the conditions is 4
What is positive integer?The positive integers are the natural numbers or also called counting numbers. These integers are also sometimes denoted by Z+. The positive integers lie on the right side of 0 on a number line. Z+ → 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,
To satisfy positive integers that will have sum of four with a 1, a 2 or a 3
The integers are
13
31
112
211
therefore there are only 4 positive integers that have sum of 4 with a 1 , a 2 and a3
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4
2
3
58%
find m angle 1
Answers
The measure of angle 1 is given as follows:
m < 1 = 42º.
How to obtain the measure of angle 1?To obtain the measure of angle 1 in the kite, we must consider that the consecutive angles are complementary, that is, the sum of their measures is of 90º.
Relative to angle 1, we have that:
m < 4 + m < 1 = 90º.
For the bottom left triangle, the internal angle measures are given as follows:
90º.m < 4.90 - 58 = 42º.Considering that the sum of the measures of the internal angles of a triangle is of 180º, the measure of angle 4 is obtained as follows:
m < 4 + 42 + 90 = 180
m < 4 = 58º.
Then the measure of angle 1 is obtained as follows:
m < 1 = 90 - 58
m < 1 = 42º.
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nellie is analyzing a quadratic function f(x) and a linear function g(x). will they intersect?
Yes, at positive x-coordinates
Yes, at negative x-coordinates
Yes, at negative and positive x-coordinates
No, they will not intersect
Answers
Yes, It intersect at positive x-coordinates.
What is Equation of line?The equation of line in point-slope form which passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, Slope (m) = (y₂ - y₁) / (x₂ - x₁)
Given that;
The function f (x) is defined in graph.
Now, The function g (x) is defined as,
⇒ y - 5 = (10 - 5) / (2 - 1) (x - 1)
⇒ y - 5 = 5 (x - 1)
⇒ y - 5 = 5x - 5
⇒ y = 5x
Clearly, By the graph of functions f (x) and g (x), both intersect at positive x - coordinate.
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1: Amelia is organising a game for a charity fête.
She has put 1 orange, 1 pink, 1 green and 2 yellow counters into a bag.
To play, each person will pay £1 and take out a counter at random.
They will then replace the counter and then take a second counter at random.
The person will win £2.50 if both counters are the same colour.
autet
Amelia expects 200 people to play the game.
How much money would Amelia expect to raise for charity?
Answers
The amount of money that Amelia is expected to raise is given as follows:
£78.13.
How to obtain the expected amount?The outcomes of a person winning, and their probabilities, as given as follows:
Two orange: 1/4 x 1/4 = 1/16.Two pink: 1/4 x 1/4 = 1/16.Two yellow: 2/4 x 2/4 = 4/16.Hence the probabilities of winning and losing are given as follows:
Winning: 6/16.Losing: 10/16.Then the distribution of earnings for each person is given as follows:
P(X = -1) = 10/16. -> Lose.P(X = 2.5) = 6/16 -> wins.Hence, considering 250 people, the expected amount raised is given as follows:
E(X) = 250/16 x (2.5 x 6 - 1 x 10)
E(X) = £78.13.
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If x = -2, what is y = ?
Answers
Answer:
y = 2
Step-by-step explanation:
If x = -2, what is y = ?
When x = -2 the line crosses the y axis at 2, so y = 2
The American flag has 50 stars, 7 red stripes, and 6 white stripes. Write a ratio to represent the ratio of stars to red stripes.
Answers
Answer:
50:7
Step-by-step explanation:
You just put ":" in between the numbers requested.
How many quarts are in8.25 gallons?
Answers
Answer:
8.25 gallan=33 quart
Step-by-step explanation:
26 gallons of gas cost $80.08. What is the unit rate for 1 gallon of gas?
A. O$2.98 per gallon
B. O$3.08 per gallon
C. O$4.16 per gallon
D. O$308.00 per gallon
Answers
Gabrielle's age is three times Mikhail's age. The sum of their ages is 64. What is Mikhail's age?
Answers
Answer:
16 years old
Step-by-step explanation:
Let's call Mikhail's age "x". Gabrielle's age is 3 times that, so her age is 3x. The sum of their ages is 64, so:
x + 3x = 64
4x = 64
x = 16
So, Mikhail's age is 16 years old.
A cargo ship contains a total of 16,770
containers that are evenly placed in 65
rows. How many containers are in each row?
ANSWER AND I'LL MARK U BRAINLIEST PLS.
Answers
Answer:258 containers
Step-by-step explanation:
Simply,
16770/65=258.
Hope this helps :]
please help me. i don't know how to do this.
Answers
- 54 is the value of x in the linear equation .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
f(X) = x² + 7x - 4
A) f(-2) + f(4) = - 14 + 40 = 26
B) f(-2) - f(4) = - 14 - 40 = -54
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How far did Mai run in her first 30 minutes
Answers
Find x. Use law of sine. Round to the nearest tenth.
Answers
Answer:
9.5
Step-by-step explanation:
Law of sine:
[tex]\frac{SideXY}{sinZ^{o}} = \frac{SideZY}{sinX^{o}} = \frac{SideXZ}{sinY^{o}}[/tex]
Sum of interior angles = 180°:
∴∠Z° = 180° - 63° - 41°
∠Z° = 76°
∴[tex]\frac{14}{sin76^{o}}[/tex]= [tex]\frac{x}{sin41^{o}}[/tex]
Cross- multiplication is applied:
(x)(sin76°) = (14)(sin41°)
x has to be isolated and made the subject of the equation:
x = [tex]\frac{[(14)(sin41^{o})]}{sin76^{o}}[/tex]
x = 9.466
x = 9.5 (Rounded to the nearest tenth)
1. An arithmetic sequence is given using the recursive definition: b₁ = 8 and b₁ =b₁-₁-3. Which of the
n-1
following is the value of b,? Show the work that leads to your answer.
(1) 14
(2) 2
(3) 6
(4) 4
Answers
Answer:
To find the value of b_n in an arithmetic sequence given by the recursive definition b_1 = 8 and b_n = b_{n-1} - 3, we can use the formula for the nth term in an arithmetic sequence:
b_n = b_1 + (n-1)d
where d is the common difference. In this case, d = -3.
So, we can plug in the values for b_1 and d to find b_n:
b_n = 8 + (n-1)(-3)
b_n = 8 - 3(n-1)
Now, to find the value of b_n for a specific n, we just need to substitute the value of n into the equation for b_n. For example, if we want to find b_14, we would substitute n = 14:
b_14 = 8 - 3(14-1)
b_14 = 8 - 3(13)
b_14 = 8 - 39
b_14 = -31
So, the value of b_14 is -31, and the answer is (1) 14.
Question 4 (10 points)
(03.06 MC)
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work. (10 points
Answers
The volume of this cylinder is 1.5 times that of the cone. The cylinder volume is 452.4 in³ while the cone volume is 301.6 in³
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Radius of cone/cylinder = diameter/2 = 8 in/2 = 4 in.
Volume of cylinder = π * radius² * height = π * (4)² * 9 = 452.4 in³
Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (4)² * 18 = 301.6 in³
The volume of this cylinder is 1.5 times that of the cone
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Which decimal is represented by the red portion of the picture?
Answers
Answer:
D
Step-by-step explanation: I did it
Rounded to 3 decimal places, what is the value of r for this data set?
Answers
The correlation coefficient r of the data given is 0.938
What is the correlation coefficient?The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables.
Given that a set of data showing the values of variables x and y, we are asked to find the correlation coefficient r of the data given,
We know that,
The correlation coefficient r is a number between and calculated to represent the linear dependence of two variables or sets of data.
Using an Excel tool :- (CORREL function) = CORREL(B3:B10,C3:C10)
We get, r = 0.938
Hence, the correlation coefficient r of the data given is 0.938
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For every 12 loaves of bread that a bakery bakes for sale, 5 cakes are baked. If 96 loaves of bread were baked, how many cakes would have been baked?
Answers
Answer:
Step-by-step explanation:
Here's a step by step explanation of how to calculate the number of cakes baked if the bakery baked 96 loaves of bread:
First, determine the number of sets of 12 loaves of bread that were baked:
96 loaves of bread ÷ 12 loaves per set = 8 sets of 12 loaves
Next, determine the number of cakes baked for each set of 12 loaves of bread:
For every set of 12 loaves, 5 cakes are baked.
Finally, multiply the number of sets by the number of cakes baked per set to find the total number of cakes baked:
8 sets × 5 cakes per set = 40 cakes
So, if the bakery baked 96 loaves of bread, they would have baked 40 cakes.
Answer:
40
Step-by-step explanation:
12 times 8 equals 96 and 5 times 8 equals 40, there for 40 cakes will be backed
